The Partition Function of ABJ Theory

Abstract

We study the partition function of the N=6 supersymmetric U(N_1)_k x U(N_2)_{-k} Chern-Simons-matter (CSM) theory, also known as the ABJ theory. For this purpose, we first compute the partition function of the U(N_1) x U(N_2) lens space matrix model exactly. The result can be expressed as a product of q-deformed Barnes G-function and a generalization of multiple q-hypergeometric function. The ABJ partition function is then obtained from the lens space partition function by analytically continuing N_2 to -N_2. The answer is given by min(N_1,N_2)-dimensional integrals and generalizes the "mirror description" of the partition function of the ABJM theory, i.e. the N=6 supersymmetric U(N)_k x U(N)_{-k} CSM theory. Our expression correctly reproduces perturbative expansions and vanishes for |N_1-N_2|>k in line with the conjectured supersymmetry breaking, and the Seiberg duality is explicitly checked for a class of nontrivial examples.

49 pages (20 pages + 5 appendices), 7 figures. v2: ref added, minor correction

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• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Fractional M2-branes
• Seiberg Duality in Chern-Simons Theory
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• On D=5 super Yang-Mills theory and (2,0) theory
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• Summing Up All Genus Free Energy of ABJM Matrix Model
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• Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• 5d quivers and their AdS(6) duals
• Exact Results on the ABJM Fermi Gas
• $N^3$-behavior from 5D Yang-Mills theory
• Anomalous radius shift in AdS(4)/CFT(3)
• New supersymmetric Wilson loops in ABJ(M) theories
• Exact ABJM Partition Function from TBA

Cited by in corpus (40)

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• Probing non-perturbative effects in M-theory
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• Direct derivation of "mirror" ABJ partition function
• ABJ Fractional Brane from ABJM Wilson Loop
• M-theoretic matrix models
• ABJM Wilson Loops in Arbitrary Representations
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Instanton Effects in Orbifold ABJM Theory
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Instanton Expansion of ABJM Partition Function
• Localization at large N in Chern-Simons-matter theories
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• On the Exact Interpolating Function in ABJ Theory
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• A matrix model for the latitude Wilson loop in ABJM theory
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• ABJ Quadrality
• Intersecting Defects and Supergroup Gauge Theory
• Exact results for ABJ Wilson loops and open-closed duality
• Two-Point Functions in ABJM Matrix Model
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Fermi gas approach to general rank theories and quantum curves
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• SU(N) q-Toda equations from mass deformed ABJM theory
• Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories
• Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• N=2 Chern-Simons-Matter Theories Without Vortices
• N=(4,4) Vector Multiplets on Curved Two-Manifolds